A hyperplane. More...
Public Types | |
enum | { AmbientDimAtCompileTime } |
typedef Matrix< Scalar, int(AmbientDimAtCompileTime)==Dynamic?Dynamic:int(AmbientDimAtCompileTime)+1, 1 > | Coefficients |
typedef Block< Coefficients, AmbientDimAtCompileTime, 1 > | NormalReturnType |
typedef NumTraits< Scalar >::Real | RealScalar |
typedef _Scalar | Scalar |
typedef Matrix< Scalar, AmbientDimAtCompileTime, 1 > | VectorType |
Public Member Functions | |
Scalar | absDistance (const VectorType &p) const |
template<typename NewScalarType > | |
ei_cast_return_type < Hyperplane, Hyperplane < NewScalarType, AmbientDimAtCompileTime > >::type | cast () const |
const Coefficients & | coeffs () const |
Coefficients & | coeffs () |
int | dim () const |
Hyperplane () | |
Hyperplane (int _dim) | |
Hyperplane (const VectorType &n, const VectorType &e) | |
Hyperplane (const VectorType &n, Scalar d) | |
Hyperplane (const ParametrizedLine< Scalar, AmbientDimAtCompileTime > ¶metrized) | |
template<typename OtherScalarType > | |
Hyperplane (const Hyperplane< OtherScalarType, AmbientDimAtCompileTime > &other) | |
VectorType | intersection (const Hyperplane &other) |
bool | isApprox (const Hyperplane &other, typename NumTraits< Scalar >::Real prec=precision< Scalar >()) const |
const NormalReturnType | normal () const |
NormalReturnType | normal () |
void | normalize (void) |
const Scalar & | offset () const |
Scalar & | offset () |
VectorType | projection (const VectorType &p) const |
Scalar | signedDistance (const VectorType &p) const |
template<typename XprType > | |
Hyperplane & | transform (const MatrixBase< XprType > &mat, TransformTraits traits=Affine) |
Hyperplane & | transform (const Transform< Scalar, AmbientDimAtCompileTime > &t, TransformTraits traits=Affine) |
Static Public Member Functions | |
static Hyperplane | Through (const VectorType &p0, const VectorType &p1) |
static Hyperplane | Through (const VectorType &p0, const VectorType &p1, const VectorType &p2) |
Protected Attributes | |
Coefficients | m_coeffs |
A hyperplane.
This is defined in the Geometry module.
A hyperplane is an affine subspace of dimension n-1 in a space of dimension n. For example, a hyperplane in a plane is a line; a hyperplane in 3-space is a plane.
_Scalar | the scalar type, i.e., the type of the coefficients |
_AmbientDim | the dimension of the ambient space, can be a compile time value or Dynamic. Notice that the dimension of the hyperplane is _AmbientDim-1. |
This class represents an hyperplane as the zero set of the implicit equation where
is a unit normal vector of the plane (linear part) and
is the distance (offset) to the origin.
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inlineexplicit |
Default constructor without initialization
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inlineexplicit |
Constructs a dynamic-size hyperplane with _dim the dimension of the ambient space
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inline |
Construct a plane from its normal n and a point e onto the plane.
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inline |
Constructs a plane from its normal n and distance to the origin d such that the algebraic equation of the plane is .
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inlineexplicit |
Constructs a hyperplane passing through the parametrized line parametrized. If the dimension of the ambient space is greater than 2, then there isn't uniqueness, so an arbitrary choice is made.
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inlineexplicit |
Copy constructor with scalar type conversion
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inline |
*this
and a point p.
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inline |
*this
with scalar type casted to NewScalarType Note that if NewScalarType is equal to the current scalar type of *this
then this function smartly returns a const reference to *this
.
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inline |
\returns a constant reference to the coefficients c_i of the plane equation:
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inline |
\returns a non-constant reference to the coefficients c_i of the plane equation:
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inline |
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inline |
*this
and other are lines.
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inline |
true
if *this
is approximately equal to other, within the precision determined by prec.
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inline |
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inline |
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inline |
normalizes *this
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inline |
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inline |
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inline |
*this
.
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inline |
*this
and a point p.
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inlinestatic |
Constructs a hyperplane passing through the two points. If the dimension of the ambient space is greater than 2, then there isn't uniqueness, so an arbitrary choice is made.
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inlinestatic |
Constructs a hyperplane passing through the three points. The dimension of the ambient space is required to be exactly 3.
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inline |
Applies the transformation matrix mat to *this
and returns a reference to *this
.
mat | the Dim x Dim transformation matrix |
traits | specifies whether the matrix mat represents an Isometry or a more generic Affine transformation. The default is Affine. |
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inline |
Applies the transformation t to *this
and returns a reference to *this
.
t | the transformation of dimension Dim |
traits | specifies whether the transformation t represents an Isometry or a more generic Affine transformation. The default is Affine. Other kind of transformations are not supported. |